# Combinatorial tangle Floer homology

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Ina Petkova, Rice University
Fine Hall 314

In joint work with Vera Vertesi, we extend the functoriality in Heegaard Floer homology by defining a Heegaard Floer invariant for tangles which satisfies a nice gluing formula. We will discuss the construction of this combinatorial invariant for tangles in S^3, D^3, and I x S^2. The special case of S^3gives back a stabilized version of knot Floer homology.